To calculate the uncertainty in speed of an electron inside the atomic nucleus, we can use the Heisenberg uncertainty principle. The Heisenberg uncertainty principle states that the product of the uncertainty in position and uncertainty in momentum of a particle is greater than or equal to the reduced Planck's constant (h-bar), which is given by:

Δx * Δp ≥ h-bar/2

In this case, we are given the size of the atomic nucleus (Δx) as 10^-14 m. We need to find the uncertainty in speed (Δv) of an electron, which is equivalent to the uncertainty in momentum (Δp) since momentum is given by the product of mass and velocity (p = m * v).

Step 1: Calculate the uncertainty in position (Δx) of the electron inside the nucleus.

Given: Δx = 10^-14 m

Step 2: Calculate the uncertainty in momentum (Δp) using the Heisenberg uncertainty principle.

Δx * Δp ≥ h-bar/2

Δp ≥ h-bar/ (2 * Δx)

We are given the value of the reduced Planck's constant (h-bar) as 6.625 * 10^-34 J * s^-1.

Δp ≥ (6.625 * 10^-34 J * s^-1) / (2 * 10^-14 m)

Step 3: Calculate the uncertainty in speed (Δv) using the uncertainty in momentum (Δp) and the mass of the electron (m_e).

Given: m_e = 9.1 * 10^-31 kg

The uncertainty in speed (Δv) is given by:

Δv = Δp / m_e

Δv ≥ [(6.625 * 10^-34 J * s^-1) / (2 * 10^-14 m)] / (9.1 * 10^-31 kg)

Simplifying the expression:

Δv ≥ (6.625 * 10^-34 J * s^-1) / (2 * 10^-14 m * 9.1 * 10^-31 kg)

Step 4: Calculate the uncertainty in speed (Δv) of the electron.

Evaluate the above expression to find the uncertainty in speed of the electron.

The uncertainty in speed of the electron inside the nucleus is equal to or greater than the calculated value.